Professional (and Somewhat Professional) Work

Research Topics – Operator and Spectral Theory, Functional Analysis, Mathematical Physics, General Relativity, Discrete Mathematics

Current Projects

• Determine the Green’s Function of K_n (the complete graph of n vertices) and Sierpinski’s Gasket.
• Inverse problems using gravitational waves.
• Parity analysis of the polydrafters.

Published (and Almost Published) Papers

1. The Green’s Function of the Sturm-Liouville Operator Acting on Graphs. PDF (Submitted)

2. Solids Whose Parallel Cross-Sections are Regular Polygons. PDF (Submitted)

3. Almost Exponential Decay of the Hamiltonian Operator Acting on Unbounded Graphs. (Draft)

Topics for Undergraduate Research:

• Modeling algor mortis with the heat equation.

· In Bulgarian solitaire of positive integer order, determine the number of maximal elements, the corresponding maximal length, and the number of connected components.

• The circular closure of a relation.
• Connected paths in recursively defined graphs.
• Minimal packings of squares into rectangles (a variation of Mrs. Perkins Quilt).

Advisor’s Past: My mathematical family tree.

Puzzles: Not word puzzles, but wooden or metal that must be manipulated to solve a particular problem. My interest is mainly in puzzles that can be solved mathematically or is related in some way to mathematics.